He definitely cared, he had a rather fatherly instinct though he'd never admit it.
As they moved through the house and he took everything in it was obvious she was struggling with something, which was not good. Living like this would only make her feel worse.
"Ah I see" relationship woes weren't his expert area but he could listen and offer a shoulder, "Do you trust him?" Haymitch asked her, "Because if you do then I'd hold onto that hope a little tighter"